establish the identity

[r8654]

Hello, I was hoping someone could help me solve a trig problem.

(1+sin(x)+cos(x))/(1+sin(x)-cos(x))=(1+cos(x))/sin(x)
or

1+sin(x)+cos(x)
______________ =
1+sin(x)-Cos(x)

1+cos(x)
sin(x)

Any help would be appreciated.

 

[tutor_joel]

Simply cross multiply here and everything cancels out. You're left with the identity sin squared + cos squared = 1

 

[r8654]

thank you. I solved it now.

 

[Loren]

If you are trying to prove the given identity, "cross multiplying" won't cut it. (In my opinion you should eliminate "cross multiply" from your vocabulary.) However, if you do some grouping you can multiply both numerator and denominator by ((1+sin(x)) + cos(x)). This will result in...
$\displaystyle \frac{(1+\sin x)^2 + 2(1+\sin x)\cos x + \cos^2x}{(1+\sin x)^2 - \cos^2x}$
Then plenty of simplification results in the desired outcome.

 

[Deleted member 4993]

Hello, I was hoping someone could help me solve a trig problem.

(1+sin(x)+cos(x))/(1+sin(x)-cos(x))=(1+cos(x))/sin(x)
or

1+sin(x)+cos(x)
______________ =
1+sin(x)-Cos(x)

1+cos(x)
sin(x)

Any help would be appreciated.

Start with left-hand-side and multiply by:
$\displaystyle \frac{1+sin(x)+cos(x)}{1+sin(x)+cos(x)}$

then simplify

 

[r8654]

thanks for the help everyone.